0195136047.pdf

740 COMMUNICATION SYSTEMS

u(t)

L C

10 kΩ m(t)

Envelope

detector

Figure P15.2.32

Equation (15.2.13) for wide-band FM iff ≥

2 W).

15.2.38A radar system uses pulses of durationDto modu-
late the amplitude of a radio carrier wave. The sys-
tem can distinguish between targets spaced apart
by a distance ofd≥cD, wherecis the velocity
of light. In view of 1/ 100 ≤B/fc≤ 1 /10, find
the minimum practical value offcso thatdmin=
30 m.
15.2.39A TDM signal of the type shown in Figure
14.2.9(b) is formed by samplingMvoice signals at
fs=8 kHz. If the TDM signal then modulates the
amplitude of a 4-MHz carrier for radio transmis-
sion, determine the upper limit onMthat satisfies
1 / 100 ≤B/fc≤ 1 /10.
15.3.1Find the minimum rate of sampling that must be
used to convert the message into digital form:
(a) If an audio message has a spectral extent of 3
kHz.
(b) If a television signal has a spectral extent of
4.5 MHz.
15.3.2If an analog message that has a spectral extent of
15 kHz is sampled at three times the Nyquist rate,
determine the sampling rate.
15.3.3The quantum levels of a quantizer are separated
by the step sizeδv= 0 .2 V, with the lowest and
highest levels of− 3 .3 V and+ 3 .3 V, respectively.
A sequence of message samples is given by− 2. 15
V,− 0 .53 V, 0.95 V, 0.17 V, and− 0 .76 V.
(a) List the quantum levels.
(b) Is the quantizer midriser or midtread?
(c) Find the corresponding sequence of the quan-
tized samples.
(d) Determine the maximum amplitude that a
message can have if the quantizer is not to
be saturated.
15.3.4When the quantum step sizeδvand the step size of
f(t) are the same as in Figure 15.3.2, the quantizer
is said to have a gain of unity. If, on the other hand,

the quantizer has a gain ofKq>1, what does that

imply?

15.3.5A symmetrically fluctuating message that has a

crest factorKCR=3 andf^2 (t)= 2 .25 V^2 is

to be quantized such that the signal-to-noise ratio

S 0 /Nq = 2700. If the quantizer is to use the

smallest number of levels that is a power of 2,

find the following:

(a) The step sizev.

(b) The binary number of levelsLb.

(c) The extreme quantum level voltages.

*15.3.6A quantizer has 130 quantum levels that exactly

span the extremes of a symmetrically fluctuating

message with step sizeδv= 0 .04 V. Determine

the following:

(a)|f(t)|max.

(b) The largest crest factor the message can have

ifS 0 /Nqmust be at least 5500.

15.3.7If a compressor in a system can change a mes-

sage crest factor from 3.2 to 2, while maintaining

its peak amplitude constant, find the decibels of

improvement in signal-to-noise ratio that can be

expected in the system.

15.3.8Determine the number of bits of a natural binary

encoder that works with the quantizer:

(a) If the extreme levels are± 3 .1 V, with a step

size of 0.2 V.

(b) If there are 128 quantum levels withδv=

0 .04 V.

15.3.9A differential encoding scheme converts the orig-

inal sequence of digits, denoted by{bk},toanew

sequence of digits, denoted by{ak}, by using the

differential encodershown in Figure P15.3.9. The

output digit in thekth interval is given byak=

ak− 1 ⊕bk, where⊕representsmodulo-2 addition

(i.e., 0⊕ 0 = 0 ; 0 ⊕ 1 = 1 ; 1 ⊕ 0 =1; and

1 ⊕ 1 =0). The new sequence is used in waveform

formatting. For the input sequence{bk}given be-

low, find the sequences{ak}and{ak− 1 }by letting